LEADER 05428nam 22006734a 450 001 9910143581703321 005 20170809162047.0 010 $a1-280-27703-3 010 $a9786610277032 010 $a0-470-32376-0 010 $a0-471-73318-0 010 $a0-471-73317-2 035 $a(CKB)1000000000355415 035 $a(EBL)232640 035 $a(OCoLC)475938712 035 $a(SSID)ssj0000125251 035 $a(PQKBManifestationID)11146550 035 $a(PQKBTitleCode)TC0000125251 035 $a(PQKBWorkID)10026744 035 $a(PQKB)11382828 035 $a(MiAaPQ)EBC232640 035 $a(EXLCZ)991000000000355415 100 $a20041015d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCombinatorial methods in discrete distributions$b[electronic resource] /$fCharalambos A. Charalambides 210 $aHoboken, N.J. $cWiley-Interscience$dc2005 215 $a1 online resource (440 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-471-68027-3 320 $aIncludes bibliographical references (p. 383-400) and indexes. 327 $aCOMBINATORIAL METHODS IN DISCRETE DISTRIBUTIONS; Contents; Preface; 1 BASIC COMBINATORICS AND PROBABILITY; 1.1 Basic counting principles; 1.2 Recurrence relations; 1.3 Finite differences; 1.4 Discrete probability; 1.5 Inclusion and exclusion principle; 1.6 Distributions and moments of random variables; 1.7 Generating functions; 1.8 Reference notes; 1.9 Exercises and complements; 2 STIRLING NUMBERS; 2.1 Introduction; 2.2 Definitions and generating functions; 2.3 Explicit expressions and recurrence relations; 2.4 Generalized factorial coefficients 327 $a2.5 Enumeration of partitions by subsets and permutations by cycles2.6 Reference notes; 2.7 Exercises and complements; 3 GENERALIZED STIRLING AND LAH NUMBERS; 3.1 Introduction; 3.2 Associated Stirling numbers; 3.3 Associated generalized factorial coefficients; 3.4 Universal generating functions; 3.5 Generalized Stirling numbers; 3.6 Generalized Lah numbers; 3.7 Reference notes; 3.8 Exercises and complements; 4 OCCUPANCY DISTRIBUTIONS; 4.1 Introduction; 4.2 A random occupancy model; 4.3 Occupancy distributions; 4.4 Particular occupancy distributions; 4.4.1 Classical occupancy distribution 327 $a4.4.2 Restricted occupancy distribution4.4.3 Pseudo-contagious occupancy distribution; 4.4.4 Restricted Bose-Einstein occupancy distribution; 4.5 Statistical applications; 4.6 A general random occupancy model; 4.7 Reference notes; 4.8 Exercises and complements; 5 SEQUENTIAL OCCUPANCY DISTRIBUTIONS; 5.1 Introduction; 5.2 A sequential random occupancy model; 5.3 Sequential occupancy distributions; 5.4 Particular sequential occupancy distributions; 5.4.1 Sequential classical occupancy distributions; 5.4.2 Sequential restricted occupancy distributions 327 $a5.4.3 Sequential pseudo-contagious occupancy distributions5.5 Statistical applications; 5.6 A reduced sequential occupancy model; 5.7 Reference notes; 5.8 Exercises and complements; 6 CONVOLUTIONS OF TRUNCATED DISTRIBUTIONS; 6.1 Introduction; 6.2 Zero truncated discrete distributions; 6.3 Some particular convolutions; 6.3.1 Zero truncated Poisson distribution; 6.3.2 Logarithmic distribution; 6.3.3 Zero truncated binomial distribution; 6.3.4 Zero truncated negative binomial distribution; 6.4 General truncated discrete distributions; 6.5 Statistical applications 327 $a6.5.1 Zero truncated power series distribution6.5.2 Left truncated power series distribution; 6.6 Reference notes; 6.7 Exercises and complements; 7 COMPOUND AND MIXTURE DISTRIBUTIONS; 7.1 Introduction; 7.2 Compound discrete distributions; 7.3 Mixture discrete distributions; 7.4 Particular compounding distributions; 7.4.1 Poisson compounding distribution; 7.4.2 Binomial compounding distribution; 7.4.3 Negative binomial compounding distribution; 7.4.4 Logarithmic compounding distribution; 7.5 Compound Poisson distributions; 7.5.1 Hermite distribution; 7.5.2 Generalized Hermite distribution 327 $a7.5.3 Po?lya-Aeppli distribution 330 $aA unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distri 410 0$aWiley series in probability and statistics. 606 $aCombinatorial analysis 606 $aDistribution (Probability theory) 608 $aElectronic books. 615 0$aCombinatorial analysis. 615 0$aDistribution (Probability theory) 676 $a511.6 676 $a519.2/4 676 $a519.24 700 $aCharalambides$b Ch. A$0893546 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143581703321 996 $aCombinatorial methods in discrete distributions$91996067 997 $aUNINA